In:
Journal of Knot Theory and Its Ramifications, World Scientific Pub Co Pte Ltd, Vol. 29, No. 02 ( 2020-02), p. 2040003-
Abstract:
We provide a physical definition of new homological invariants [Formula: see text] of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on [Formula: see text] times a 2-disk, [Formula: see text], whose Hilbert space of BPS states plays the role of a basic building block in categorification of various partition functions of 3d [Formula: see text] theory [Formula: see text]: [Formula: see text] half-index, [Formula: see text] superconformal index, and [Formula: see text] topologically twisted index. The first partition function is labeled by a choice of boundary condition and provides a refinement of Chern–Simons (WRT) invariant. A linear combination of them in the unrefined limit gives the analytically continued WRT invariant of [Formula: see text]. The last two can be factorized into the product of half-indices. We show how this works explicitly for many examples, including Lens spaces, circle fibrations over Riemann surfaces, and plumbed 3-manifol ds.
Type of Medium:
Online Resource
ISSN:
0218-2165
,
1793-6527
DOI:
10.1142/S0218216520400039
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2020
detail.hit.zdb_id:
1108304-9
SSG:
17,1
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